Factors, Primes & Composite Numbers

Definitions Product – An answer to a multiplication problem. 5 x 6 = 30 Product

Factor – – a number that is multiplied by another to give a product. – all the whole numbers that can be divided exactly into a given number –the facts you multiply together 5 x 6 = 30 Factors

What are the factors? 6 x 7 = 42 7 x 9 = 63 8 x 6 = 48 4 x 9 = 36 6 & 7 7 & 9 8 & 6 4 & 9

Prime Number – a number with exactly two factors, 1 and itself 7 7 is prime because the only numbers that will divide into it evenly are 1 and 7. 1 x 7 Factors 1, 7

Examples of Prime Numbers 2, 3, 5, 7, 11, 13, 17, 19 Special Note: One is not a prime number.

Composite number – a number that has more than two factors. 8 The factors of 8 are 1, 2, 4, 8 1 x 8 2 x 4 8 is a composite number because it has more than two factors.

Examples of Composite Numbers 4, 6, 8, 9, 10, 12, 14, 15 Special Note: Every whole number from 2 on is either composite or prime.

Our Lonely 1 Special Note: One is not a prime nor a composite number. It is not prime because it does not have exactly two different factors. It is not composite because it does not have more than 2 factors.

Definition Prime Factorization – A way to write a composite number as the product of prime factors. 2 x 2 x 3 = 12 or 2 2 x 3 = 12

How to Do Prime Factorization Using a Factor Tree 48 Step 1 – Start with a composite number. Step 2 – beginning dividing with the first prime number that is divisible by

Step 3 – divide your largest numbers by the first prime number that it is divisible by Step 4 – Find factors of these numbers until all factors are prime numbers

Step 5 – List the prime factorization of the number x 2 x 2 x 2 x 3 or 2 4 X 3

Prime factor this number 4 2 x 2 2 = 4 2 = 4

Prime factor this number 6 2 x 3= 6

Prime factor this number 8 2 x 4 2 = 8 3 = 8 2 x 2 x 2 = 8

Prime factor this number 9 3 x 3= 9 3 = 9 2

Prime factor this number 10 2 x 5= 10

Prime factor this number 12 3 x 4 2 x 3 = 12 2 = 12 3 x 2 x 2 = 12 2 x 2 x 3 = 12

Prime factor this number 14 2 x 7= 14

Prime factor this number 15 3 x 5= 15

Prime factor this number 16 4 x 4 2 = 16 4 = 16 2 x 2 x 2 x 2 = 16

Prime factor this number 18 3 x 6 2 x 3 = 18 2 = 18 3 x 2 x 3 = 18 2 x 3 x 3 = 18

Prime factor this number 20 4 x 5 2 x 5 = 20 2 = 20 2 x 2 x 5 = 20

Prime factor this number 21 3 x 7= 21

Prime factor this number 22 2 x 11= 22